Enhanced error estimator based on a nearly equilibrated moving least squares recovery technique for FEM and XFEM

In this paper a new technique aimed to obtain accurate estimates of the error in energy norm using a moving least squares (MLS) recovery-based procedure is presented. We explore the capabilities of a recovery technique based on an enhanced MLS fitting, which directly provides continuous interpolated fields, to obtain estimates of the error in energy norm as an alternative to the superconvergent patch recovery (SPR). Boundary equilibrium is enforced using a nearest point approach that modifies the MLS functional. Lagrange multipliers are used to impose a nearly exact satisfaction of the internal equilibrium equation. The numerical results show the high accuracy of the proposed error estimator

On stability of discretizations of the Helmholtz equation (extended version)

We review the stability properties of several discretizations of the Helmholtz equation at large wavenumbers. For a model problem in a polygon, a complete $k$-explicit stability (including $k$-explicit stability of the continuous problem) and convergence theory for high order finite element methods is developed. In particular, quasi-optimality is shown for a fixed number of degrees of freedom per wavelength if the mesh size $h$ and the approximation order $p$ are selected such that $kh/p$ is sufficiently small and $p = O(\log k)$, and, additionally, appropriate mesh refinement is used near the vertices. We also review the stability properties of two classes of numerical schemes that use piecewise solutions of the homogeneous Helmholtz equation, namely, Least Squares methods and Discontinuous Galerkin (DG) methods. The latter includes the Ultra Weak Variational Formulation

Alterations to nuclear architecture and genome behavior in senescent cells.

The organization of the genome within interphase nuclei, and how it interacts with nuclear structures is important for the regulation of nuclear functions. Many of the studies researching the importance of genome organization and nuclear structure are performed in young, proliferating, and often transformed cells. These studies do not reveal anything about the nucleus or genome in nonproliferating cells, which may be relevant for the regulation of both proliferation and replicative senescence. Here, we provide an overview of what is known about the genome and nuclear structure in senescent cells. We review the evidence that nuclear structures, such as the nuclear lamina, nucleoli, the nuclear matrix, nuclear bodies (such as promyelocytic leukemia bodies), and nuclear morphology all become altered within growth-arrested or senescent cells. Specific alterations to the genome in senescent cells, as compared to young proliferating cells, are described, including aneuploidy, chromatin modifications, chromosome positioning, relocation of heterochromatin, and changes to telomeres

NuRD suppresses pluripotency gene expression to promote transcriptional heterogeneity and lineage commitment

Transcriptional heterogeneity within embryonic stem cell (ESC) populations has been suggested as a mechanism by which a seemingly homogeneous cell population can initiate differentiation into an array of different cell types. Chromatin remodeling proteins have been shown to control transcriptional variability in yeast and to be important for mammalian ESC lineage commitment. Here we show that the Nucleosome Remodeling and Deacetylation (NuRD) complex, which is required for ESC lineage commitment, modulates both transcriptional heterogeneity and the dynamic range of a set of pluripotency genes in ESCs. In self-renewing conditions, the influence of NuRD at these genes is balanced by the opposing action of self-renewal factors. Upon loss of self-renewal factors, the action of NuRD is sufficient to silence transcription of these pluripotency genes, allowing cells to exit self-renewal. We propose that modulation of transcription levels by NuRD is key to maintaining the differentiation responsiveness of pluripotent cells

A Toy Model for Testing Finite Element Methods to Simulate Extreme-Mass-Ratio Binary Systems

Extreme mass ratio binary systems, binaries involving stellar mass objects orbiting massive black holes, are considered to be a primary source of gravitational radiation to be detected by the space-based interferometer LISA. The numerical modelling of these binary systems is extremely challenging because the scales involved expand over several orders of magnitude. One needs to handle large wavelength scales comparable to the size of the massive black hole and, at the same time, to resolve the scales in the vicinity of the small companion where radiation reaction effects play a crucial role. Adaptive finite element methods, in which quantitative control of errors is achieved automatically by finite element mesh adaptivity based on posteriori error estimation, are a natural choice that has great potential for achieving the high level of adaptivity required in these simulations. To demonstrate this, we present the results of simulations of a toy model, consisting of a point-like source orbiting a black hole under the action of a scalar gravitational field.Comment: 29 pages, 37 figures. RevTeX 4.0. Minor changes to match the published versio

The radial arrangement of the human chromosome 7 in the lymphocyte cell nucleus is associated with chromosomal band gene density

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ Springer-Verlag 2008.In the nuclei of human lymphocytes, chromosome territories are distributed according to the average gene density of each chromosome. However, chromosomes are very heterogeneous in size and base composition, and can contain both very gene-dense and very gene-poor regions. Thus, a precise analysis of chromosome organisation in the nuclei should consider also the distribution of DNA belonging to the chromosomal bands in each chromosome. To improve our understanding of the chromatin organisation, we localised chromosome 7 DNA regions, endowed with different gene densities, in the nuclei of human lymphocytes. Our results showed that this chromosome in cell nuclei is arranged radially with the gene-dense/GC-richest regions exposed towards the nuclear interior and the gene-poorest/GC-poorest ones located at the nuclear periphery. Moreover, we found that chromatin fibres from the 7p22.3 and the 7q22.1 bands are not confined to the territory of the bulk of this chromosome, protruding towards the inner part of the nucleus. Overall, our work demonstrates the radial arrangement of the territory of chromosome 7 in the lymphocyte nucleus and confirms that human genes occupy specific radial positions, presumably to enhance intra- and inter-chromosomal interaction among loci displaying a similar expression pattern, and/or similar replication timing

Efficient recovery-based error estimation for the smoothed finite element method for smooth and singular linear elasticity

[EN] An error control technique aimed to assess the quality of smoothed finite element approximations is presented in this paper. Finite element techniques based on strain smoothing appeared in 2007 were shown to provide significant advantages compared to conventional finite element approximations. In particular, a widely cited strength of such methods is improved accuracy for the same computational cost. Yet, few attempts have been made to directly assess the quality of the results obtained during the simulation by evaluating an estimate of the discretization error. Here we propose a recovery type error estimator based on an enhanced recovery technique. The salient features of the recovery are: enforcement of local equilibrium and, for singular problems a ¿smooth + singular¿ decomposition of the recovered stress. We evaluate the proposed estimator on a number of test cases from linear elastic structural mechanics and obtain efficient error estimations whose effectivities, both at local and global levels, are improved compared to recovery procedures not implementing these features.Stephane Bordas would like to thank the partial financial support of the Royal Academy of Engineering and of the Leverhulme Trust for his Senior Research Fellowship Towards the next generation surgical simulators as well as the financial support for Octavio A. Gonzalez-Estrada and Stephane Bordas from the UK Engineering Physical Science Research Council (EPSRC) under grant EP/G042705/1 Increased Reliability for Industrially Relevant Automatic Crack Growth Simulation with the eXtended Finite Element Method. Stephane Bordas also thanks partial financial support of the European Research Council Starting Independent Research Grant (ERC Stg grant agreement No. 279578) and the FP7 Initial Training Network Funding under grant number 289361 "Integrating Numerical Simulation and Geometric Design Technology, INSIST". This work has been carried out within the framework of the research project DPI2010-20542 of the Ministerio de Ciencia e Innovacion (Spain). The financial support from Universitat Politecnica de Valencia, PROMETEO/2012/023 and Generalitat Valenciana are also acknowledged.González Estrada, OA.; Natarajan, S.; J.J. Ródenas; Nguyen-Xuan, H.; Bordas, S. (2013). Efficient recovery-based error estimation for the smoothed finite element method for smooth and singular linear elasticity. Computational Mechanics. 52(1):37-52. https://doi.org/10.1007/s00466-012-0795-6S3752521Liu GR, Dai KY, Nguyen TT (2006) A smoothed finite element method for mechanics problems. 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Commun Numer Methods Eng 25: 19–34Nguyen-Xuan H, Rabczuk T, Bordas S, Debongnie JF (2008) A smoothed finite element method for plate analysis. Comput Methods Appl Mech Eng 197: 1184–1203Nguyen NT, Rabczuk T, Nguyen-Xuan H, Bordas S (2008) A smoothed finite element method for shell analysis. Comput Methods Appl Mech Eng 198: 165–177Bordas SPA, Rabczuk T, Hung NX, Nguyen VP, Natarajan S, Bog T, óuan DM, Hiep NV (2010) Strain smoothing in FEM and XFEM. Comput Struct 88(23–24): 1419–1443. doi: 10.1016/j.compstruc.2008.07.006Bordas SP, Natarajan S, Kerfriden P, Augarde CE, Mahapatra DR, Rabczuk T, Pont SD (2011) On the performance of strain smoothing for óuadratic and enriched finite element approximations (XFEM/GFEM/PUFEM). Int J Numer Methods Biomed Eng 86: 637–666Liu G, Nguyen-Thoi T, Nguyen-Xuan H, Dai K, Lam K (2009) On the essence and the evaluation of the shape functions for the smoothed finite element method (SFEM). 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Int J Numer Methods Eng 60: 861–890Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique. Int J Numer Methods Eng 33(7): 1331–1364Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity. Int J Numer Methods Eng 33(7): 1365–1382Wiberg NE, Abdulwahab F (1993) Patch recovery based on superconvergent derivatives and eóuilibrium. Int J Numer Methods Eng 36(16): 2703–2724. doi: 10.1002/nme.1620361603Blacker T, Belytschko T (1994) Superconvergent patch recovery with eóuilibrium and conjoint interpolant enhancements. Int J Numer Methods Eng 37(3): 517–536Stein E, Ramm E, Rannacher R (2003) Error-controlled adaptive finite elements in solid mechanics. Wiley, ChichesterDuflot M, Bordas SPA (2008) A posteriori error estimation for extended finite elements by an extended global recovery. 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In: Khalili N, Valliappan S, Li ó, Russell A (eds) 9th World congress on computational mechanics (WCCM9). 4th Asian Pacific Congress on computational methods (APCOM2010). Centre for Infrastructure Engineering and SafetyRódenas JJ, González-Estrada OA, Díez P, Fuenmayor FJ (2007) Upper bounds of the error in the extended finite element method by using an eóuilibrated-stress patch recovery technique. In: International conference on adaptive modeling and simulation (ADMOS 2007). International Center for Numerical Methods in Engineering (CIMNE), pp 210–213Menk A, Bordas S (2010) Numerically determined enrichment function for the extended finite element method and applications to bi-material anisotropic fracture and polycrystals. Int J Numer Methods Eng 83: 805–828Menk A, Bordas S (2011) Crack growth calculations in solder joints based on microstructural phenomena with X-FEM. 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Flux norm approach to finite dimensional homogenization approximations with non-separated scales and high contrast

We consider divergence-form scalar elliptic equations and vectorial equations for elasticity with rough ($L^\infty(\Omega)$, $\Omega \subset \R^d$) coefficients $a(x)$ that, in particular, model media with non-separated scales and high contrast in material properties. We define the flux norm as the $L^2$ norm of the potential part of the fluxes of solutions, which is equivalent to the usual $H^1$-norm. We show that in the flux norm, the error associated with approximating, in a properly defined finite-dimensional space, the set of solutions of the aforementioned PDEs with rough coefficients is equal to the error associated with approximating the set of solutions of the same type of PDEs with smooth coefficients in a standard space (e.g., piecewise polynomial). We refer to this property as the {\it transfer property}. A simple application of this property is the construction of finite dimensional approximation spaces with errors independent of the regularity and contrast of the coefficients and with optimal and explicit convergence rates. This transfer property also provides an alternative to the global harmonic change of coordinates for the homogenization of elliptic operators that can be extended to elasticity equations. The proofs of these homogenization results are based on a new class of elliptic inequalities which play the same role in our approach as the div-curl lemma in classical homogenization.Comment: Accepted for publication in Archives for Rational Mechanics and Analysi

Nucleolus: the fascinating nuclear body

Nucleoli are the prominent contrasted structures of the cell nucleus. In the nucleolus, ribosomal RNAs are synthesized, processed and assembled with ribosomal proteins. RNA polymerase I synthesizes the ribosomal RNAs and this activity is cell cycle regulated. The nucleolus reveals the functional organization of the nucleus in which the compartmentation of the different steps of ribosome biogenesis is observed whereas the nucleolar machineries are in permanent exchange with the nucleoplasm and other nuclear bodies. After mitosis, nucleolar assembly is a time and space regulated process controlled by the cell cycle. In addition, by generating a large volume in the nucleus with apparently no RNA polymerase II activity, the nucleolus creates a domain of retention/sequestration of molecules normally active outside the nucleolus. Viruses interact with the nucleolus and recruit nucleolar proteins to facilitate virus replication. The nucleolus is also a sensor of stress due to the redistribution of the ribosomal proteins in the nucleoplasm by nucleolus disruption. The nucleolus plays several crucial functions in the nucleus: in addition to its function as ribosome factory of the cells it is a multifunctional nuclear domain, and nucleolar activity is linked with several pathologies. Perspectives on the evolution of this research area are proposed